3d Geometry

The plane passing through the line \(L: l x-y+3(1-l) z=1, x+2 y-z=2\) and perpendicular to the plane \(3 x+2 y+z=6\) is \(3 x-8 y+7 z=4\). If \(\theta\) is the acute angle between the line \(L\) and the \(y\)-axis, then \(415 \cos ^{2} \theta\) is equal to _____________.